Ultrasonic Sound

The term "ultrasonic" applied to sound refers to anything above the frequencies
of audible sound, and nominally includes anything over 20,000 Hz. Frequencies used
for medical diagnostic ultrasound scans extend to 10 MHz and beyond.

Sounds in the range 20-100kHz are commonly used for communication and
navigation by bats,dolphins, and some other species. Much higher frequencies, in the
range 1-20 MHz, are used for medical ultrasound. Such sounds are produced
by ultrasonic transducers. A wide variety of medical diagnostic applications use both
the echo time and the Doppler shift of the reflected sounds to measure the distance to
internal organs and structures and the speed of movement of those structures. Typical
is the echocardiogram, in which a moving image of the heart's action is produced in
video form with false colors to indicate the speed and direction of blood flow and
heart valve movements. Ultrasound imaging near the surface of the body is capable of
resolutions less than a millimeter. The resolution decreases with the depth of
penetration since lower frequencies must be used (the attenuation of the waves in
tissue goes up with increasing frequency.) The use of longer wavelengths implies
lower resolution since the maximum resolution of any imaging process is proportional
to the wavelength of the imaging wave.

Bats and Ultrasound

Bats use ultrasonic sound for navigation. Their ability to catch flying insects while
flying full speed in pitch darkness is astounding. Their sophisticated echolocation
permits them to distinguish between a moth (supper) and a falling leaf.

About 800 species of bats grouped into 17 families. The ultrasonic signals utilized by
these bats fall into three main categories. 1. short clicks, 2. Frequency-swept pulses,
and 3. constant frequency pulses. There are two suborders, Megachiroptera and
Microchiroptera. Megas use short clicks, Micros use the other two. Tongue clicks
produce click pairs separated by about 30ms, with 140-430 ms between pairs. (Sales
and Pye, Ultrasonic Communication by Animals). 10-60 kHz in frequency swept
clicks. One kind of bat, the verspertilionidae, have frequency swept pulses 78 kHz to
39 kHz in 2.3 ms. Emits pulses 8 to 15 times a second, but can increase to 150-200/s
when there is a tricky maneuver to be made.
 Cetacean Sound
Orcas produce a wide variety of clicks, whistles and pulsed calls. They vary in
frequency from 1 to 25 kHz. Individual pods of whales have their own distinctive
dialect of calls, similar to songbirds. Some such calls are known to be stable over a
period of 10 years. Humpback whales produce a variety of moans, snores, and groans
that are repeated to form what we might call songs. The frequency of these songs
range from about 40 Hz to 5 kHz. Singing whales are usually solitary males who
exhibit it in a shallow smooth-bottomed area where sound propagates well. They are
interpreted as territorial and mating calls. Whales are also known to produce some
very intense low frequency sounds which they may use to stun or disorient small fish
for prey. Bottlenose dolphins produce sounds in the range 7 to 15 kHz which are
continuously variable in pitch. In addition, they produce short burst from 20 to 170
kHz, presumably for better echolocation.

A dolphin's clicks come from small knobs near its blowhole. There are no vocal cords.

Decibels
The sound intensity I may be expressed in decibels above the standard threshold of
hearing I0 . The expression is

The logarithm involved is just the power of ten of the sound intensity expressed as a
multiple of the threshold of hearing intensity. Example: If I= 10,000 times the
threshold, then the ratio of the intensity to the threshold intensity is 10 4, the power of
ten is 4, and the intensity is 40 dB:
The factor of 10 multiplying the logarithm makes it decibels instead of Bels, and is
included because about 1 decibel is the just noticeable difference (JND) in sound
intensity for the normal human ear.

Decibels provide a relative measure of sound intensity. The unit is based on powers of
10 to give a manageable range of numbers to encompass the wide range of the human
hearing response, from the standard threshold of hearing at 1000 Hz to the threshold
of pain at some ten trillion times that intensity.

Another consideration which prompts the use of powers of 10 for sound measurement
is the rule of thumb for loudness: it takes about 10 times the intensity to sound twice
as loud.
 Decibels and Logarithms
The decibel scale is a reflection of the logarithmic response of the human ear to
changes in sound intensity:

The logarithm to the base 10 used in this expression is just the power of 10 of the
quantity in brackets according to the basic definition of the logarithm:

Examples:
 Decibel Calculation
The sound intensity in decibels above the standard threshold of hearing is calculated
as alogarithm. If the intensity as a multiple of threshold is

= x 10^

then the intensity in decibels is given by

dB

Decibels can also be used to express the relative intensity of two sounds. If one is
expressed as a multiple of the other:

IA = xIB = x 10^ xIB

then the difference in decibels is given by

IA = dB above IB
If you know the sound level in decibels at one distance in an open area, then you can
estimate the dB level at another distance by making use of the inverse square law.
 Variations in Difference Threshold

The above data are from Backus, suggesting that the JND in dB is less for more
intense sounds. He is citing Harvey Fletcher's "Speech and Hearing in
Communication"(1953),p146, as the actual data source. But you can do a test for
yourself of pairs of tones that are stated to be 2dB different at theMcGraw-Hill site.
This site discusses "Weber's law", which states just the opposite of the implication of
the above curves.

Reflection of Sound
The reflection of sound follows the law "angle of incidence equals angle of
reflection", sometimes called the law of reflection. The same behavior is observed
with light and other waves, and by the bounce of a billiard ball off the bank of a table.
The reflected waves can interfere with incident waves, producing patterns of
constructive and destructive interference. This can lead to resonances called standing
waves in rooms. It also means that the sound intensity near a hard surface is enhanced
because the reflected wave adds to the incident wave, giving a pressure amplitude that
is twice as great in a thin "pressure zone" near the surface. This is used in pressure
zone microphones to increase sensitivity. The doubling of pressure gives a 6 decibel
increase in the signal picked up by the microphone. Reflection of waves
in strings and air columns are essential to the production of resonant standing waves
in those systems.

Phase Change Upon Reflection

The phase of the reflected sound waves from hard surfaces and the reflection of string
waves from their ends determines whether the interference of the reflected and
incident waves will be constructive or destructive. For string waves at the ends of
strings there is a reversal of phase and it plays an important role in
producing resonance in strings. Since the reflected wave and the incident wave add to
each other while moving in opposite directions, the appearance of propagation is lost
and the resulting vibration is called a standing wave.

When sound waves in air (pressure waves) encounter a hard surface, there is no phase
change upon reflection. That is, when the high pressure part of a sound wave hits the
wall, it will be reflected as a high pressure, not a reversed phase which would be a low
pressure. Keep in mind that when we talk about the pressure associated with a sound
wave, a positive or "high" pressure is one that is above the ambient atmospheric
pressure and a negative or "low" pressure is just one that is below atmospheric
pressure. A wall is described as having a higher "acoustic impedance" than the air,
and when a wave encounters a medium of higher acoustic impedance there is no phase
change upon reflection.

On the other hand, if a sound wave in a solid strikes an air boundary, the pressure
wave which reflects back into the solid from the air boundary will experience a phase
reversal - a high-pressure part reflecting as a low-pressure region. That is, reflections
off a lower impedance medium will be reversed in phase.

Besides manifesting itself in the "pressure zone" in air near a hard surface, the nature
of the reflections contribute to standing waves in rooms and in the air columns which
make up musical instruments.
The conditions which lead to a phase change on one end but not the other can also be
envisioned with a string if one presumes that the loose end of a string is constrained to
move only transverse to the string. The loose end would represent an interface with a
smaller effective impedance and would produce no phase change for the transverse
wave. In many ways, the string and the air column are just the inverse of each other.
 Pressure Zone
The sound intensity near a hard surface is enhanced because the reflected wave adds
to the incident wave, giving a pressure amplitude that is twice as great in a thin
"pressure zone" near the surface. This is used in pressure zone microphones to
increase sensitivity. The doubling of pressure gives a 6 decibel increase in the signal
picked up by the microphone.

This is an attempt to visualize the phenomenon of the pressure zone in

terms of the dynamics of the air molecules involved in transporting the
sound energy. The air molecules are of course in ceaseless motion just
from thermal energy and have energy as a result of the atmospheric
pressure. The energy involved in sound transport is generally very tiny
compared to that overall energy. If you visualize the velocity vectors
shown in the illustration as just that additional energy which associated
with the sound energy in the longitudinal wave, then we can argue that
the horizontal components of the velocities will just be reversed upon
collision with the wall. Presuming the collisions with the wall to
beelastic, no energy is lost in the collisions.

Viewing the collection of molecules as a "fluid", we can invoke the idea

that the internal pressure of a fluid is a measure of energy density. The
energy of the molecules reflecting off the wall adds to that of the
molecules approaching the wall in the volume very close to the wall,
effectively doubling the energy density and hence the pressure
associated with the sound wave.
 Refraction of Sound
Refraction is the bending of waves when they enter a medium where their speed is
different. Refraction is not so important a phenomenon with sound as it is with light
where it is responsible forimage formation by lenses, the eye, cameras, etc.
But bending of sound waves does occur and is an interesting phenomena in sound

These visualizations may help in understanding the nature of refraction. A column of

troops approaching a medium where their speed is slower as shown will turn toward
the right because the right side of the column hits the slow medium first and is
therefore slowed down. The marchers on the left, perhaps oblivious to the plight of
their companions, continue to march ahead full speed until they hit the slow medium.

Not only does the direction of march change, the separation of the marchers is
decreased. When applied to waves, this implies that the direction of propagation of the
wave is deflected toward the right and that the wavelength of the wave is decreased.
From the basic wave relationship, v=fλ , it is clear that a slower speed must shorten
the wavelength since the frequency of the wave is determined by its source and does
not change.

Another visualization of refraction can come from the steering of various types of
tractors, construction equipment, tanks and other tracked vehicle. If you apply the
right brake, the vehicle turns right because you have slowed down one side of the
vehicle without slowing down the other.
 Refraction of Sound

If the air above the earth is

warmer than that at the surface,
sound will be bent back
downward toward the surface
by refraction.

Sound propagates in all directions from a point source. Normally, only that which is
initially directed toward the listener can be heard, but refraction can bend sound
downward. Normally, only the direct sound is received. But refraction can add some
additional sound, effectively amplifying the sound. Natural amplifiers can occur over
cool lakes.
 Refraction of Sound
Early morning fishermen may be the persons most familiar with the refraction of
sound. Consider that you have gone out to a lake before dawn. Just as the sun rises
over a cool lake, you may hear someone speak to you, saying "Good morning!". You
look around and can't see anyone. You are just about at the point of questioning your
sanity anyway, being out at this time of the morning, so you decide to ignore it. But
the voice comes again, "Good morning". Finally you locate the other nut who has
gotten up at this hour, far across the lake -- much further than you could normally hear
a voice. That fisherman is aware of the early morning lake's effect on sound
transmission. The cool water keeps the air near the water cool, but the early sun has
begun to heat the air higher up, creating a "thermal inversion". The fact that the speed
of sound is faster in warmer air bends some sound back downward toward you -
sound that would not reach your ear under normal circumstances. This natural
amplification over cool bodies of water is one of the few natural examples of sound
refraction.
 Diffraction of Sound
Diffraction: the bending of waves around small* obstacles and
the spreading out of waves beyond small* openings.
* small compared to the wavelength

Important parts of our experience with sound involve diffraction. The fact that you
can hear sounds around corners and around barriers involves both diffraction and
reflection of sound. Diffraction in such cases helps the sound to "bend around" the
obstacles. The fact that diffraction is more pronounced with longer wavelengths
implies that you can hear low frequencies around obstacles better than high
frequencies, as illustrated by the example of a marching band on the street. Another
common example of diffraction is the contrast in sound from a close lightning strike
and a distant one. The thunder from a close bolt of lightning will be experienced as a
sharp crack, indicating the presence of a lot of high frequency sound. The thunder
from a distant strike will be experienced as a low rumble since it is the long
wavelengths which can bend around obstacles to get to you. There are other factors
such as the higher air absorption of high frequencies involved, but diffraction plays a
part in the experience.
You may perceive diffraction to have a dual nature, since the same phenomenon
which causes waves to bend around obstacles causes them to spread out past small
openings. This aspect of diffraction also has many implications. Besides being able to
hear the sound when you are outside the door as in the illustration above, this
spreading out of sound waves has consequences when you are trying to soundproof a
room. Good soundproofing requires that a room be well sealed, because any openings
will allow sound from the outside to spread out in the room - it is surprising how
much sound can get in through a small opening. Good sealing of loudspeaker cabinets
is required for similar reasons.

Another implication of diffraction is the fact that a wave which is much longer than
the size of an obstacle, like the post in the auditorium above, cannot give you
information about that obstacle. A fundamental principle of imaging is that you
cannot see an object which is smaller than the wavelength of the wave with which you
view it. You cannot see a virus with a light microscope because the virus is smaller
than the wavelength of visible light. The reason for that limitation can be visualized
with the auditorium example: the sound waves bend in and reconstruct the wavefront
past the post. When you are several sound wavelengths past the post, nothing about
the wave gives you information about the post. So your experience with sound can
give you insights into the limitations of all kinds of imaging processes.
 Doppler Effect
You hear the high pitch of the siren of the approaching ambulance, and notice that its
pitch drops suddenly as the ambulance passes you. That is called the Doppler effect.
 Doppler Effect
When a vehicle with a siren passes you, a noticeable drop in the pitch of the sound of
the siren will be observed as the vehicle passes. This is an example of the Doppler
effect. An approaching source moves closer during period of the sound wave so the
effective wavelength is shortened, giving a higher pitch since the velocity of the wave
is unchanged. Similarly the pitch of a receding sound source will be lowered.
 Doppler Wavelength Change
The speed of sound is determined by the medium in which it is traveling, and
therefore is the same for a moving source. But the frequency and wavelength are
changed. The wavelengths for a moving source are given by the relationships below.
It is sometimes convenient to express the change in wavelength as a fraction of the
source wavelength for a stationary source:
 Doppler Effect Frequency Calculation
At temperature C= F

the sound speed in air is m/s.

If the source frequency is Hz

and the velocity of the source is m/s = mi/hr

then for an approaching source the frequency is Hz

and for a receding source the frequency is Hz.

Note: The frequency will default to A4 (440 Hz) and the temperature will default to
20 C if those values are not entered. Any parameters can be changed.
 Periodic Motion
Periodic motion of some source object is necessary to produce a sustained musical
sound (i.e., one with definite pitch and quality). For example, to produce a standard
musical A (440 Hz), the source object must sustain periodic motion at 440 vibrations
per second with a tolerance of less than 1 Hz -- the normal human ear can detect the
difference between 440 Hz and 441 Hz. The conditions necessary for periodic motion
are

1. elasticity - the capacity to return precisely to the original configuration after

being distorted.
o a. a definite equilibrium configuration
o b. a restoring force to bring the system back to equilibrium
2. A source of energy.

Fortunately, it is not hard to find vibrators which meet these conditions, hence the
richness in variety of musical sound sources.

Terms for describing periodic motion.

A mass on a spring is an example of periodic motion with a single frequency

called simple harmonic motion.
 Description of Periodic Motion
Motion which repeats itself precisely can be described with the following terms:

 Period: the time required to complete a full cycle, T in seconds/cycle

 Frequency: the number of cycles per second, f in 1/seconds or Hertz (Hz)

 Amplitude: the maximum displacement from equilibrium A

and if the periodic motion is in the form of a traveling wave, one needs also

 Velocity of propagation: v

 Wavelength: repeat distance of wave λ.

 Period, Frequency and Amplitude
In a plot of periodic motion as a
function of time, the period can be If the period T = s
seen as the repeat time for the motion. T = ms
The frequency is the reciprocal of the
period. T= x 10^ s

then the frequency f = Hz

f= kHz
f= MHz
f= x 10^ Hz
 Temporary Threshold Shifts
Loud concerts can cause temporary shifts in the threshold of hearing in the mid
frequency region. In one study, a group of 20 young adult females were exposed to
sound at 110 dB for 60 minutes, 3 minutes on and 1 minute off to simulate a concert.
The results were:

Number Temporary
Frequency
out of 20 threshold shift

1 > 15 dB shift 2000 Hz

4 > 20 dB shift 3000 Hz
11 > 20 dB shift 4000 Hz
8 > 20 dB shift 6000 Hz
Emphasizing the wide variability of such tests, 2 of the subjects showed greater than
40 dB threshold shift at 4000 Hz while 9 showed less than 20 dB. None showed a loss
(shift) above the guideline at 1000Hz or 8000 Hz, so the shifts are concentrated in
the maximum sensitivity range of human hearing. There is no firmly established
correlation between temporary threshold shifts and permanent threshold shifts.
However, it is prudent to point out that if permanent hearing damage followed the
pattern of the temporary threshold shifts, it would be the worst kind of damage
because it would diminish hearing acuity in the frequency range that is most important
for the understanding of human speech.
 Audiometry of Rock Musicians
Since controlled studies of human subjects which might do harm cannot be ethically
carried out, one alternative is to find persons who voluntarily subject themselves to
very loud sounds and measure their hearing. Such an effort was made in Britain with a
group of 42 musicians who agreed to a hearing screen every three years.

Date Subjects Assessment of hearing

95% of whom showed no measurable
1968 42 rock musicians
hearing loss.
10 rock musicians
none showed more than 10 dB of threshold
1971 (Rock musicians are apparently a transient
shift.
species.)
2 showed > 15 dB loss at 3,4 kHz
1974 6 rock musicians:
1 with 35 dB loss at 3 kHz

The study is not very meaningful because of the small numbers, but it is consistent
with the study of temporary threshold shifts in that the damage was in the mid-range
frequencies.
 Animal Studies
Some animal studies have attempted to assess hearing damage from loud sounds. One
British study subjected a group of 6 chinchillas to rock music for 2.5 hours at 1 meter
from a loudspeaker (average 107 dBA) and then did histological studies of their inner
ears. There was a large variation in the the amount of damage done to their inner ears.
Perhaps those with a small amount of damage were in the corner of their cage with
their paws over their ears. The only significant outcome seems to be the variability - if
there is wide variability in the damage to these animal's ears, it would not be
surprising if the susceptibility of human's ears also show wide variability in the
vulnerability to damage. The problem is that you would not know whether you are
particularly susceptible to damage until you had sustained damage.

Can you limit sound levels?

In 1973 the Leeds City Council in Britain limited their discoteques to a sound level of
96 dBA peak by a license restriction. In the face of legal action a year later, the
restriction was removed. The Association of Ballrooms mounted the successful legal
challenge by showing that the the equivalent continuous sound level could not be
assessed visually with a sound level meter and that the peak intensity of concerts
exceeded the average by about 10 dBA. The controversy spawned numerous studies
of concert sound levels. Typical results:

91-115 dB average level

Measured rock groups:
3 of 51 groups > 115 dB average
Rock groups averaged 100 dBA and 106 dB
U. of Michigan study:
range 84 - 111 dBA